Imaging lens

ABSTRACT

A four element lens system for use with an imaging sensor includes first, second, third, and fourth lens elements and an optical filter that are arranged sequentially in order from an object side to an imaging side. The lens elements are coated with an anti-reflective film. The lens system further includes an optical filter that is disposed at a distance from the imaging sensor. The lens elements are relatively positioned to each other to satisfy specific conditions. The lens elements further include thickness to diameters ratios that satisfy specific conditions.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No. 13/757,634, filed Feb. 1, 2013, entitled “Imaging Lens,” which claims priority to Chinese Patent Application No. 201210328950.8, filed Sep. 7, 2012. The disclosure of U.S. application Ser. No. 13/757,634 is incorporated herein by reference.

BACKGROUND

The present disclosure relates to an imaging lens and an imaging lens system having the same, more particularly to an imaging lens with four lens elements and to an imaging lens system having the same.

In recent years, various electronic devices have been designed to include imaging lenses and image sensors for image-capturing and video-recording capabilities. To improve portability and imaging performance while reducing dimensions and weights of the electronic devices, different combinations of lenses are installed in electronic devices that have embedded charge coupled device (CCD) sensors or complementary metal oxide semiconductor (CMOS) image sensors. There is thus a need for compact imaging lenses and imaging lens systems that provide improved image quality. Compactness in a lens system is determined by the size of the clear aperture diameters of the lens elements in the lens system. In the description below, the diameter of a lens element is referred to its clear aperture diameter for the sake of brevity.

U.S. Pat. No. 7,453,654 discloses imaging lenses with four lens elements. Each of the imaging lenses has a unique combination and arrangement of lens elements with different shapes to thereby achieve a specific combination of optical characteristics. However, in achieving the specific combination of optical characteristics, certain aspects of optical performance are comprised. Therefore, the need to develop other imaging lenses with better combinations of optical characteristics still exists in the market.

SUMMARY

Certain embodiments of the present invention provide imaging lenses and systems with a desired combination of optical characteristics.

According to an embodiment of the present invention, an imaging lens includes first, second, third, and fourth lens elements arranged sequentially in order from an object side to an imaging side, each of the first, second, third, and fourth lens elements having an object-side surface facing toward the object side, and an imaging-side surface facing toward the imaging side. The imaging lens satisfies the conditions of vd1−vd2>30, 0.5<d1avg/d2avg<0.9, 0.4 <d3avg/d4avg<0.7, wherein vd1 and vd2 are Abbe numbers of the respective first and second lens elements, and d1avg, d2avg, d3avg, and d4avg are average diameters of the first, second, third, and fourth lens elements.

According to another embodiment of the present invention, an imaging lens system has in order from an object side to an imaging side an aperture stop, a first lens element, a second lens element, a third lens element, and a fourth lens element arranged behind the aperture stop in sequence. Each lens element has an object-side diameter and an imaging-side diameter. The object-side diameter is equal to or smaller than the imaging-side diameter. The aperture stop is configured to pass light and has a circular-shaped opening. The circular-shaped opening has a diameter that is equal to or smaller than the object-side diameter of the first lens element. The first lens element has a first Abbe number and the second lens element has a second Abbe number. The first Abbe number is greater than the second Abbe number by at least 30. The object-side and imaging-side surfaces of each lens element can be coated with an anti-reflective coating.

According to yet another embodiment of the present invention, a lens system includes first, second, third, and fourth lens elements that are arranged in order from an object side to an imaging side. The four lens elements are sequentially arranged on an optical axis. The lens system further includes an optical filter disposed between the fourth lens element and the imaging sensor along the optical axis. Each of the first, second, third, and fourth lens elements has an object-side surface facing toward the object side, and an imaging-side surface facing toward the imaging side. The optical filter has an object-side surface and disposed at a distance of 0.4 mm from the imaging-side of the fourth lens element. In an embodiment, the imaging-side surface of the first lens element and the object-side surface of the second lens element have an air gap of 0.07 mm, the imaging-side surface of the second lens element and the object-side surface of the third lens element have an air gap of 0.34 mm, and the imaging-side surface of the third lens element and the object-side surface of the fourth lens element has an air gap of 0.06 mm. In an embodiment, the first lens element may have a thickness of 0.42 mm, the second lens element may have a thickness of 0.26 mm, the third lens element may have a thickness of 0.435 mm, and the fourth lens element may have a thickness of 0.3 mm. In an embodiment, the optical filter may have a thickness of 0.3 mm and may be disposed at a distance about 0.4 mm of the imaging-side surface of the forth lens element.

The following detailed description together with the accompanying drawings will provide a better understanding of the nature and advantages of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating some terms used in the present description.

FIG. 2 is a schematic diagram illustrating lens elements, filter, imaging sensor and the optical axis in accordance with an imaging lens system.

FIG. 3 is a schematic diagram defining the terminology used in an imaging lens system.

FIG. 4 is a cross-sectional view of a lens element to define sag values.

FIG. 5 is a schematic diagram illustrating TV distortion of an imaging lens system.

FIG. 6 is a schematic diagram illustrating a relationship between an imaging sensor, an associated image sensor circle and a maximum image circle according to an embodiment of the present invention.

DETAILED DESCRIPTION

The term “lens element” is herein defined as a single transparent mass of refractive material having two opposed refracting surfaces. The term “diameter” is referred to as the “clear aperture” or “clear aperture diameter” of a lens element. The term “clear aperture”, “clear aperture diameter”, and “diameter” will be alternatively used throughout the specification. The term “total track length” or “TTL” is defined as a distance from an object-side surface of the first lens element to an imaging plane. A “sag” is the displacement of the surface of the lens from a plane transverse (perpendicular) to the optical axis and can be measured at different radial distances from the optical axis. FIG. 1 shows an example of two different lens elements having different sag values at the 25 percent point, 50 percent point, 75 percent point, and at the 100 percent point from the optical axis, where the percentages are relative to the radius of the lens in the perpendicular plane.

Referring to FIG. 2, an imaging lens system 200, according to an embodiment of the present invention, may include a cover glass or window 2, first, second, third, and fourth lens elements 3, 4, 5, 6, and an optical filter 7 arranged in the given order from an object side to an imaging side. Each of the first, second, third, and fourth lens elements 3, 4, 5, 6 has an object-side surface 31, 41, 51, 61, facing toward the object side, and an imaging-side surface 32, 42, 52, 62, facing toward the imaging side. In some embodiments, aperture stop 1 may be disposed at object-side surface 21 of cover glass or window 2. When light from a target object enters imaging lens system 200, it passes through aperture stop 1, cover glass or window 2, lens elements 3 through 6, and optical filter 7 in the given order, and forms an image at an imaging plane 8 which may be a surface of an imaging sensor.

In some embodiments, aperture stop 1 is made of an opaque material. A central opening 11 through aperture stop 1 may be circular shaped and have a diameter that is smaller than the diameter of the object-side surface 31 of the first lens element. In an exemplary embodiment, the diameter of the aperture stop is about 0.91 mm and the diameter of object-side surface 31 of the first lens element is about 1.01 mm. In another embodiment, aperture stop 1 may be disposed between cover glass 2 and object-side surface 31 of the first lens element 3.

Each lens element has two shaped surfaces that converge or diverge light. Each lens element is made out of an optically transparent material, such as glass or plastic. The refractive index of the lens material and curvature of the shaped surface define the light refraction. The surface curvature of each lens element can be defined by a set of sag values. In an embodiment, the set of sag values of each lens element can be provided in a table format to a computer database for manufacturing a lens element.

Referring still to FIG. 2, optical filter 7 has an object-side surface 71 facing toward the object side, and an imaging-side surface 72 facing toward the imaging side. In some embodiments, the optical filter may be an infrared filter that passes light having a wavelength lower than 0.8 microns and suppresses transmission of light having wavelengths greater than 0.8 microns. Each of the four lens elements may have a refractive index greater than 1.5. In some embodiments, the object-side surface and the imaging-side surface of the first, second, third, and fourth lens elements are coated with an anti-reflective coating.

In some embodiments, the relative position of the lens elements to each other, the diameter to thickness ratio of each lens element, the ratio between the sum of the air gaps and the total track length are factors in achieving good optical performance. In some embodiments an air gap between the lens elements is needed to facilitate proper focusing of incident light. Referring to FIG. 3, s1 is an air gap between the imaging-side surface of the first lens element and the object-side surface of the second lens element, s2 is an air gap between the imaging-side surface of the second lens element and the object-side surface of the third lens element, s3 is an air gap between the imaging-side surface of the third lens element and the object-side surface of the fourth lens element, and s4 is an air gap between the imaging-side surface of the fourth lens element and the object-side surface of the optical filter. Additionally, imaging plane 8 is placed at a distance s5 from optical filter 7, as shown in FIG. 3. If the imaging plane is placed at a distance larger than 0.4 mm from the optical filter, the imaging sensor may generate an inaccurate image due to possible loss of light with a given chief ray angle (CRA). In an embodiment, the chief ray angle is less than 28 degrees.

Referring still to FIG. 3, t1 is a thickness of first lens element 3 that is measured from the object-side surface at the optical axis to the imaging-side surface at the optical axis. Similarly, t2 is a thickness of second lens element 4 measured at the optical axis, t3 is a thickness of third lens element 5 measured at the optical axis, and t4 is a thickness of fourth lens element 6 measured at the optical axis. Each lens element may have one or more flanges formed around its periphery and extending outwardly away from the optical axis. The flanges may be used to mount the lens element to a lens barrel (not shown). The effective diameter (i.e., the “clear aperture” or “clear aperture diameter”) of the object-side surface of first lens element 3 is designated d1, and the effective diameter of the imaging-side surface of first lens element 3 is designated d2. The effective diameter is defined as the diameter of the surface of the lens element that may contribute to the optical performance of the lens element. In other words, the effective diameter may not include the flange at the outer periphery of the lens element.

Hereinafter, the effective diameter is referred as the diameter. Similarly, the diameter of the object-side surface of second lens element 4 is designated d3, and the diameter of the imaging-side surface of second lens element 4 is designated d4; the diameter of the object-side surface of third lens element 5 is designated d5, and the diameter of the imaging-side surface of third lens element 5 is designated d6; the diameter of the object-side surface of fourth lens element 6 is designated d7, and the diameter of the imaging-side surface of fourth lens element 6 is designated d8.

Table 1 provides design parameters of a lens system according to an embodiment of the present invention.

TABLE 1 Refractive lens index Thickness (mm) Air gap (mm) Diameter (mm) first 1.54 t1 = 0.420 s1 = 0.07 d1 = 1.011 d2 = 1.194 second 1.63 t2 = 0.26 s2 = 0.34 d3 = 1.302 d4 = 1.336 third 1.54 t3 = 0.435 s3 = 0.06 d5 = 1.457 d6 = 1.714 fourth 1.53 t4 = 0.3 s4 = 0.40 d7 = 2.711 d8 = 2.903

Referring to Table 1 and FIG. 3, the thickness of the lens element is measured from the object-side surface to the imaging-side surface at the optical axis. The air gap is measured from the imaging-side of a lens element to the object-side of an adjacent lens element along the optical axis. In an embodiment, the first lens element 3 has a thickness of 0.42 mm along the optical axis, and the air gap distance (measured at the optical axis) from the imaging-side surface of first lens element 3 to the object-side surface of second lens element 4 is 0.07 mm along the optical axis. The second lens element 4 has a thickness of 0.26 mm along the optical axis. The third lens element 5 has a thickness of 0.435 mm along the optical axis, and the fourth lens element 6 has a thickness of 0.3 mm along the optical axis. In an embodiment, the optical filter is interposed between fourth lens element 6 and imaging sensor 8. The optical filter may have a thickness of about 0.3 mm and disposed at a distance of about 0.4 mm from the imaging-side surface of fourth lens element 6 and at a distance of about 0.3 to 0.4 mm from the imaging sensor.

In an embodiment, the diameter d1 of the object-side surface of first lens element 3 is 1.011 mm. The diameter d2 of the imaging-side surface of first lens element 3 is 1.194 mm. Similarly, the diameter d3 of the object-side surface of second lens element 4 is 1.302 mm and the diameter d4 of the imaging-side surface of second lens element 4 is 1.336 mm. The last 4 rows of Table 1 provide the respective object-side and imaging-side diameters d5, d6, d7, and d8 of third and fourth lens elements. In an embodiment, the thickness of the lens elements has a manufacturing tolerance of less than ±2 to less than ±6 microns depending on the power of the lens. In an embodiment, the tilt of the lens elements is less than ±0.1 degree.

Referring still to FIG. 3, the lens elements are rotationally symmetric about the optical axis. The optical performance of lens system 300 is generally related to the particular object-side and imaging-side surface shapes of the lens elements. These surfaces can be characterized by sag values at various radial distances from the optical axis.

Tables 2 through 5 include sag values of the lens elements 3, 4, 5 and 6, respectively. The sag values are in microns. The “normalized lens Ht” in the first and fourth columns denotes the normalized relative distance of lens element 3 from the optical axis. In other words, 0.0% corresponds to the location at the optical axis, 50.0% and 100.0% correspond to the respective one half and the full radius of lens element 3 in relation to the optical axis. As the lens element is rotationally symmetric about the optical axis, the surface of the lens element is sufficient represented by sag values for the normalized lens height from the optical axis. The sag tables are provided in sufficient detail to be used for the fabrication of the lens elements using a numerically controlled machining tool. The thus obtained lens elements may have a sag tolerance less than ±2 to less than ±6 microns depending on the lens power. It should be noted that, in actual manufacturing, a slope function is used to assure that surface slopes and tolerance variations do not cause step functions in the shape of the lens surface. It should be noted that the tolerance between adjacent sag values may alternate between positive and negative values for not causing steps on the surface of the lens element.

Table 2 contains sag data for fabricating lens element 3. The “Min Sag 3” and the “Max Sag 3” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 3. Similarly, the “Min Sag 4” and the “Max Sag 4” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 3. In an embodiment, the lens element 3 needs to be within the minimum and maximum sag values to ensure a given optical performance. Sag data in Table 2 is given in mm.

TABLE 2 Normal- Normal- ized ized Lens Ht Min Sag 3 Max Sag 3 Lens Ht Min Sag 4 Max Sag 4 0.0% −0.001000 0.001000 0.0% −0.001000 0.001000 2.0% −0.000969 0.001031 1.7% −0.001018 0.000982 3.9% −0.000875 0.001125 3.3% −0.001071 0.000929 5.9% −0.000718 0.001282 5.0% −0.001159 0.000841 7.8% −0.000499 0.001501 6.7% −0.001283 0.000717 9.8% −0.000217 0.001782 8.3% −0.001443 0.000556 11.8% 0.000127 0.002125 10.0% −0.001640 0.000360 13.7% 0.000533 0.002531 11.7% −0.001873 0.000127 15.7% 0.001000 0.002998 13.3% −0.002143 −0.000144 17.6% 0.001530 0.003526 15.0% −0.002451 −0.000452 19.6% 0.002120 0.004116 16.7% −0.002797 −0.000798 21.6% 0.002771 0.004767 18.3% −0.003182 −0.001184 23.5% 0.003483 0.005478 20.0% −0.003608 −0.001610 25.5% 0.004255 0.006249 21.7% −0.004074 −0.002077 27.5% 0.005087 0.007079 23.3% −0.004583 −0.002585 29.4% 0.005978 0.007970 25.0% −0.005134 −0.003137 31.4% 0.006928 0.008918 26.7% −0.005729 −0.003733 33.3% 0.007936 0.009926 28.3% −0.006370 −0.004374 35.3% 0.009002 0.010990 30.0% −0.007057 −0.005063 37.3% 0.010126 0.012112 31.7% −0.007793 −0.005799 39.2% 0.011305 0.013291 33.3% −0.008578 −0.006585 41.2% 0.012540 0.014525 35.0% −0.009415 −0.007423 43.1% 0.013830 0.015813 36.7% −0.010305 −0.008313 45.1% 0.015174 0.017155 38.3% −0.011249 −0.009259 47.1% 0.016570 0.018550 40.0% −0.012250 −0.010261 49.0% 0.018017 0.019996 41.7% −0.013310 −0.011321 51.0% 0.019515 0.021492 43.3% −0.014430 −0.012443 52.9% 0.021060 0.023036 45.0% −0.015612 −0.013627 54.9% 0.022653 0.024627 46.7% −0.016859 −0.014876 56.9% 0.024290 0.026263 48.3% −0.018173 −0.016191 58.8% 0.025969 0.027941 50.0% −0.019556 −0.017576 60.8% 0.027689 0.029659 51.7% −0.021010 −0.019032 62.7% 0.029446 0.031416 53.3% −0.022537 −0.020561 64.7% 0.031239 0.033207 55.0% −0.024140 −0.022166 66.7% 0.033064 0.035031 56.7% −0.025819 −0.023848 68.6% 0.034917 0.036883 58.3% −0.027578 −0.025610 70.6% 0.036796 0.038761 60.0% −0.029418 −0.027453 72.5% 0.038696 0.040661 61.7% −0.031342 −0.029379 74.5% 0.040614 0.042578 63.3% −0.033349 −0.031390 76.5% 0.042546 0.044509 65.0% −0.035443 −0.033487 78.4% 0.044485 0.046449 66.7% −0.037623 −0.035671 80.4% 0.046428 0.048391 68.3% −0.039893 −0.037944 82.4% 0.048368 0.050331 70.0% −0.042251 −0.040306 84.3% 0.050298 0.052262 71.7% −0.044699 −0.042759 86.3% 0.052211 0.054176 73.3% −0.047238 −0.045302 88.2% 0.054099 0.056065 75.0% −0.049868 −0.047936 90.2% 0.055951 0.057918 76.7% −0.052589 −0.050661 92.2% 0.057757 0.059726 78.3% −0.055402 −0.053479 94.1% 0.059502 0.061473 80.0% −0.058309 −0.056391 96.1% 0.061171 0.063145 81.7% −0.061310 −0.059398 98.0% 0.062744 0.064722 83.3% −0.064409 −0.062502 100.0% 0.063612 0.065591 85.0% −0.067610 −0.065708 86.7% −0.070918 −0.069023 88.3% −0.074345 −0.072457 90.0% −0.077904 −0.076024 91.7% −0.081617 −0.079748 93.3% −0.085518 −0.083663 95.0% −0.089656 −0.087818 96.7% −0.094106 −0.092293 98.3% −0.098990 −0.097214 100.0% −0.103022 −0.101288

In accordance with Table 2, lens element 3 may have an average sag value of 20 microns (0.020 mm) at 50 point and an average sag value of 65 microns (0.065 mm) at 100 point of the clear aperture of the object-side. The ratio between the sag value at 50 point and at 100 point satisfies the following conditions: 0.2<sag3(50)/sag3(100)<0.6 or preferably 0.25<sag3(50)/sag3(100)<0.50.

Table 3 contains sag data for fabricating lens element 4. The “Min Sag 5” and the “Max Sag 5” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 3. Similarly, the “Min Sag 6” and the “Max Sag 6” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 4. In an embodiment, the lens element 4 needs to be within the minimum and maximum sag values to ensure a given optical performance. Sag values in Table 3 are given in mm.

TABLE 3 Normal- Normal- ized ized Lens Ht Min Sag 5 Max Sag 5 Lens Ht Min Sag 6 Max Sag 6 0.0% −0.001000 0.001000 0.0% −0.001000 0.001000 1.5% −0.000989 0.001011 1.5% −0.000963 0.001037 3.0% −0.000957 0.001043 3.0% −0.000854 0.001146 4.5% −0.000903 0.001097 4.5% −0.000671 0.001329 6.1% −0.000827 0.001173 6.0% −0.000414 0.001585 7.6% −0.000731 0.001269 7.5% −0.000085 0.001914 9.1% −0.000613 0.001387 9.0% 0.000318 0.002316 10.6% −0.000475 0.001525 10.4% 0.000794 0.002791 12.1% −0.000317 0.001683 11.9% 0.001343 0.003340 13.6% −0.000138 0.001861 13.4% 0.001966 0.003962 15.2% 0.000059 0.002059 14.9% 0.002663 0.004658 16.7% 0.000275 0.002275 16.4% 0.003433 0.005426 18.2% 0.000509 0.002508 17.9% 0.004276 0.006269 19.7% 0.000760 0.002759 19.4% 0.005193 0.007184 21.2% 0.001027 0.003026 20.9% 0.006184 0.008173 22.7% 0.001309 0.003308 22.4% 0.007248 0.009236 24.2% 0.001605 0.003604 23.9% 0.008384 0.010371 25.8% 0.001913 0.003912 25.4% 0.009594 0.011579 27.3% 0.002233 0.004232 26.9% 0.010877 0.012860 28.8% 0.002562 0.004561 28.4% 0.012232 0.014213 30.3% 0.002899 0.004898 29.9% 0.013659 0.015638 31.8% 0.003243 0.005242 31.3% 0.015157 0.017134 33.3% 0.003592 0.005590 32.8% 0.016727 0.018701 34.8% 0.003943 0.005942 34.3% 0.018366 0.020339 36.4% 0.004295 0.006294 35.8% 0.020076 0.022046 37.9% 0.004646 0.006645 37.3% 0.021854 0.023822 39.4% 0.004995 0.006994 38.8% 0.023701 0.025666 40.9% 0.005339 0.007337 40.3% 0.025614 0.027577 42.4% 0.005676 0.007675 41.8% 0.027594 0.029555 43.9% 0.006005 0.008004 43.3% 0.029639 0.031597 45.5% 0.006325 0.008324 44.8% 0.031747 0.033703 47.0% 0.006633 0.008632 46.3% 0.033919 0.035872 48.5% 0.006930 0.008929 47.8% 0.036153 0.038103 50.0% 0.007214 0.009213 49.3% 0.038447 0.040395 51.5% 0.007485 0.009485 50.7% 0.040800 0.042746 53.0% 0.007744 0.009743 52.2% 0.043212 0.045155 54.5% 0.007990 0.009990 53.7% 0.045682 0.047622 56.1% 0.008226 0.010226 55.2% 0.048208 0.050146 57.6% 0.008453 0.010452 56.7% 0.050789 0.052725 59.1% 0.008673 0.010673 58.2% 0.053426 0.055359 60.6% 0.008891 0.010890 59.7% 0.056118 0.058048 62.1% 0.009109 0.011109 61.2% 0.058864 0.060791 63.6% 0.009334 0.011333 62.7% 0.061665 0.063590 65.2% 0.009571 0.011570 64.2% 0.064522 0.066443 66.7% 0.009826 0.011826 65.7% 0.067434 0.069353 68.2% 0.010109 0.012108 67.2% 0.070405 0.072321 69.7% 0.010427 0.012426 68.7% 0.073435 0.075348 71.2% 0.010791 0.012790 70.1% 0.076527 0.078437 72.7% 0.011211 0.013209 71.6% 0.079685 0.081591 74.2% 0.011697 0.013695 73.1% 0.082912 0.084813 75.8% 0.012263 0.014259 74.6% 0.086213 0.088110 77.3% 0.012921 0.014916 76.1% 0.089593 0.091485 78.8% 0.013683 0.015677 77.6% 0.093059 0.094946 80.3% 0.014563 0.016554 79.1% 0.096618 0.098500 81.8% 0.015573 0.017562 80.6% 0.100279 0.102154 83.3% 0.016726 0.018711 82.1% 0.104052 0.105919 84.8% 0.018031 0.020013 83.6% 0.107946 0.109806 86.4% 0.019500 0.021476 85.1% 0.111975 0.113826 87.9% 0.021138 0.023109 86.6% 0.116151 0.117992 89.4% 0.022950 0.024915 88.1% 0.120490 0.122319 90.9% 0.024937 0.026895 89.6% 0.125007 0.126824 92.4% 0.027094 0.029046 91.0% 0.129720 0.131523 93.9% 0.029410 0.031356 92.5% 0.134648 0.136435 95.5% 0.031870 0.033809 94.0% 0.139812 0.141581 97.0% 0.034446 0.036380 95.5% 0.145233 0.146982 98.5% 0.037103 0.039035 97.0% 0.150934 0.152661 100.0% 0.037460 0.039391 98.5% 0.156941 0.158644 100.0% 0.162236 0.163918

Table 4 contains sag data for fabricating lens element 5. The “Min Sag 7” and the “Max Sag 7” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 3. Similarly, the “Min Sag 8” and the “Max Sag 8” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 5. In an embodiment, the lens element 5 needs to be within the minimum and maximum sag values to ensure a given optical performance. Sag values in Table 4 are given in mm.

TABLE 4 Normal- Normal- ized ized Lens Ht Min Sag 7 Max Sag 7 Lens Ht Min Sag 8 Max Sag 8 0.0% −0.001500 0.001500 0.0% −0.001500 0.001500 1.4% −0.001534 0.001466 1.2% −0.001592 0.001407 2.7% −0.001634 0.001365 2.3% −0.001869 0.001129 4.1% −0.001802 0.001197 3.5% −0.002329 0.000667 5.5% −0.002036 0.000963 4.7% −0.002971 0.000020 6.8% −0.002337 0.000661 5.8% −0.003795 −0.000808 8.2% −0.002704 0.000294 7.0% −0.004799 −0.001817 9.6% −0.003135 −0.000139 8.1% −0.005980 −0.003004 11.0% −0.003632 −0.000636 9.3% −0.007335 −0.004366 12.3% −0.004192 −0.001197 10.5% −0.008863 −0.005902 13.7% −0.004815 −0.001821 11.6% −0.010561 −0.007607 15.1% −0.005500 −0.002508 12.8% −0.012424 −0.009479 16.4% −0.006246 −0.003255 14.0% −0.014450 −0.011515 17.8% −0.007051 −0.004061 15.1% −0.016635 −0.013709 19.2% −0.007915 −0.004927 16.3% −0.018976 −0.016060 20.5% −0.008835 −0.005849 17.4% −0.021468 −0.018563 21.9% −0.009812 −0.006827 18.6% −0.024108 −0.021213 23.3% −0.010842 −0.007858 19.8% −0.026893 −0.024008 24.7% −0.011924 −0.008942 20.9% −0.029817 −0.026943 26.0% −0.013057 −0.010077 22.1% −0.032877 −0.030014 27.4% −0.014238 −0.011260 23.3% −0.036070 −0.033218 28.8% −0.015467 −0.012490 24.4% −0.039391 −0.036550 30.1% −0.016740 −0.013765 25.6% −0.042836 −0.040006 31.5% −0.018055 −0.015082 26.7% −0.046403 −0.043583 32.9% −0.019411 −0.016440 27.9% −0.050087 −0.047277 34.2% −0.020806 −0.017835 29.1% −0.053884 −0.051085 35.6% −0.022236 −0.019267 30.2% −0.057791 −0.055002 37.0% −0.023700 −0.020732 31.4% −0.061805 −0.059026 38.4% −0.025195 −0.022229 32.6% −0.065921 −0.063153 39.7% −0.026718 −0.023753 33.7% −0.070137 −0.067378 41.1% −0.028268 −0.025304 34.9% −0.074450 −0.071700 42.5% −0.029841 −0.026877 36.0% −0.078855 −0.076115 43.8% −0.031434 −0.028472 37.2% −0.083349 −0.080618 45.2% −0.033045 −0.030084 38.4% −0.087930 −0.085207 46.6% −0.034671 −0.031711 39.5% −0.092593 −0.089879 47.9% −0.036310 −0.033350 40.7% −0.097335 −0.094629 49.3% −0.037958 −0.034999 41.9% −0.102153 −0.099454 50.7% −0.039613 −0.036654 43.0% −0.107042 −0.104351 52.1% −0.041272 −0.038313 44.2% −0.112000 −0.109316 53.4% −0.042932 −0.039973 45.3% −0.117021 −0.114344 54.8% −0.044591 −0.041631 46.5% −0.122103 −0.119432 56.2% −0.046245 −0.043285 47.7% −0.127241 −0.124575 57.5% −0.047893 −0.044932 48.8% −0.132429 −0.129770 58.9% −0.049531 −0.046570 50.0% −0.137665 −0.135010 60.3% −0.051158 −0.048196 51.2% −0.142942 −0.140291 61.6% −0.052771 −0.049809 52.3% −0.148255 −0.145608 63.0% −0.054368 −0.051406 53.5% −0.153599 −0.150955 64.4% −0.055949 −0.052985 54.7% −0.158969 −0.156327 65.8% −0.057510 −0.054546 55.8% −0.164357 −0.161717 67.1% −0.059052 −0.056087 57.0% −0.169757 −0.167118 68.5% −0.060574 −0.057607 58.1% −0.175163 −0.172524 69.9% −0.062074 −0.059107 59.3% −0.180568 −0.177928 71.2% −0.063555 −0.060587 60.5% −0.185963 −0.183322 72.6% −0.065016 −0.062047 61.6% −0.191342 −0.188698 74.0% −0.066459 −0.063489 62.8% −0.196695 −0.194048 75.3% −0.067885 −0.064915 64.0% −0.202015 −0.199364 76.7% −0.069298 −0.066328 65.1% −0.207293 −0.204637 78.1% −0.070702 −0.067731 66.3% −0.212519 −0.209857 79.5% −0.072101 −0.069130 67.4% −0.217684 −0.215015 80.8% −0.073500 −0.070529 68.6% −0.222779 −0.220102 82.2% −0.074906 −0.071935 69.8% −0.227794 −0.225107 83.6% −0.076326 −0.073356 70.9% −0.232719 −0.230022 84.9% −0.077770 −0.074801 72.1% −0.237544 −0.234836 86.3% −0.079247 −0.076280 73.3% −0.242260 −0.239540 87.7% −0.080769 −0.077804 74.4% −0.246856 −0.244123 89.0% −0.082348 −0.079386 75.6% −0.251322 −0.248576 90.4% −0.083999 −0.081041 76.7% −0.255650 −0.252889 91.8% −0.085737 −0.082784 77.9% −0.259830 −0.257054 93.2% −0.087580 −0.084633 79.1% −0.263853 −0.261062 94.5% −0.089546 −0.086607 80.2% −0.267712 −0.264905 95.9% −0.091656 −0.088725 81.4% −0.271399 −0.268576 97.3% −0.093930 −0.091011 82.6% −0.274908 −0.272069 98.6% −0.096393 −0.093487 83.7% −0.278233 −0.275378 100.0% −0.098763 −0.095872 84.9% −0.281370 −0.278499 86.0% −0.284317 −0.281431 87.2% −0.287071 −0.284171 88.4% −0.289634 −0.286721 89.5% −0.292008 −0.289082 90.7% −0.294197 −0.291261 91.9% −0.296210 −0.293264 93.0% −0.298055 −0.295101 94.2% −0.299746 −0.296784 95.3% −0.301298 −0.298330 96.5% −0.302731 −0.299759 97.7% −0.304067 −0.301092 98.8% −0.305335 −0.302358 100.0% −0.306217 −0.303239

Table 5 contains sag data for fabricating lens element 6. The “Min Sag 9” and the “Max Sag 9” of the second and third columns are the minimum and maximum sag values of the object-side surface of lens element 3. Similarly, the “Min Sag 10” and the “Max Sag 10” of the fifth and sixth columns are the minimum and maximum sag values of the imaging-side surface of lens element 6. In an embodiment, the lens element 6 needs to be within the minimum and maximum sag values to ensure a given optical performance. Sag data in Table 5 is given in mm.

TABLE 5 Normal- Normal- ized ized Min Sag Max Sag Lens Ht Min Sag 9 Max Sag 9 Lens Ht 10 10 0.0% −0.003000 0.003000 0.0% −0.003000 0.003000 0.7% −0.002969 0.003031 0.7% −0.002904 0.003095 1.5% −0.002874 0.003125 1.4% −0.002616 0.003380 2.2% −0.002717 0.003281 2.1% −0.002137 0.003853 2.9% −0.002498 0.003500 2.7% −0.001471 0.004512 3.7% −0.002217 0.003780 3.4% −0.000620 0.005354 4.4% −0.001875 0.004121 4.1% 0.000411 0.006374 5.1% −0.001471 0.004523 4.8% 0.001618 0.007569 5.9% −0.001008 0.004985 5.5% 0.002995 0.008933 6.6% −0.000485 0.005506 6.2% 0.004536 0.010459 7.4% 0.000096 0.006085 6.8% 0.006234 0.012143 8.1% 0.000735 0.006722 7.5% 0.008083 0.013976 8.8% 0.001430 0.007414 8.2% 0.010075 0.015952 9.6% 0.002179 0.008161 8.9% 0.012203 0.018064 10.3% 0.002983 0.008962 9.6% 0.014460 0.020306 11.0% 0.003838 0.009815 10.3% 0.016838 0.022669 11.8% 0.004745 0.010719 11.0% 0.019331 0.025146 12.5% 0.005701 0.011672 11.6% 0.021931 0.027732 13.2% 0.006704 0.012673 12.3% 0.024631 0.030417 14.0% 0.007754 0.013720 13.0% 0.027424 0.033197 14.7% 0.008848 0.014811 13.7% 0.030304 0.036064 15.4% 0.009984 0.015944 14.4% 0.033264 0.039012 16.2% 0.011161 0.017118 15.1% 0.036298 0.042035 16.9% 0.012377 0.018332 15.8% 0.039400 0.045126 17.6% 0.013629 0.019582 16.4% 0.042564 0.048281 18.4% 0.014917 0.020866 17.1% 0.045786 0.051493 19.1% 0.016237 0.022184 17.8% 0.049058 0.054757 19.9% 0.017588 0.023533 18.5% 0.052378 0.058069 20.6% 0.018968 0.024911 19.2% 0.055739 0.061423 21.3% 0.020375 0.026315 19.9% 0.059137 0.064815 22.1% 0.021806 0.027745 20.5% 0.062568 0.068241 22.8% 0.023260 0.029197 21.2% 0.066027 0.071695 23.5% 0.024734 0.030669 21.9% 0.069510 0.075175 24.3% 0.026227 0.032160 22.6% 0.073014 0.078675 25.0% 0.027735 0.033667 23.3% 0.076535 0.082194 25.7% 0.029258 0.035189 24.0% 0.080069 0.085725 26.5% 0.030792 0.036723 24.7% 0.083613 0.089268 27.2% 0.032337 0.038266 25.3% 0.087163 0.092817 27.9% 0.033889 0.039818 26.0% 0.090717 0.096370 28.7% 0.035447 0.041376 26.7% 0.094271 0.099924 29.4% 0.037009 0.042937 27.4% 0.097822 0.103476 30.1% 0.038573 0.044500 28.1% 0.101368 0.107023 30.9% 0.040136 0.046064 28.8% 0.104906 0.110563 31.6% 0.041697 0.047625 29.5% 0.108433 0.114092 32.4% 0.043254 0.049183 30.1% 0.111946 0.117608 33.1% 0.044805 0.050734 30.8% 0.115444 0.121109 33.8% 0.046349 0.052279 31.5% 0.118924 0.124592 34.6% 0.047883 0.053814 32.2% 0.122383 0.128055 35.3% 0.049405 0.055338 32.9% 0.125820 0.131496 36.0% 0.050916 0.056849 33.6% 0.129233 0.134913 36.8% 0.052411 0.058346 34.2% 0.132618 0.138303 37.5% 0.053891 0.059827 34.9% 0.135975 0.141665 38.2% 0.055354 0.061292 35.6% 0.139301 0.144997 39.0% 0.056798 0.062738 36.3% 0.142595 0.148296 39.7% 0.058223 0.064163 37.0% 0.145854 0.151561 40.4% 0.059626 0.065568 37.7% 0.149077 0.154790 41.2% 0.061007 0.066951 38.4% 0.152262 0.157981 41.9% 0.062364 0.068311 39.0% 0.155407 0.161134 42.6% 0.063698 0.069646 39.7% 0.158512 0.164245 43.4% 0.065006 0.070956 40.4% 0.161573 0.167313 44.1% 0.066289 0.072241 41.1% 0.164590 0.170338 44.9% 0.067545 0.073499 41.8% 0.167562 0.173316 45.6% 0.068774 0.074730 42.5% 0.170486 0.176248 46.3% 0.069976 0.075934 43.2% 0.173361 0.179130 47.1% 0.071150 0.077110 43.8% 0.176186 0.181963 47.8% 0.072296 0.078258 44.5% 0.178959 0.184744 48.5% 0.073414 0.079378 45.2% 0.181679 0.187472 49.3% 0.074504 0.080469 45.9% 0.184345 0.190146 50.0% 0.075566 0.081533 46.6% 0.186956 0.192765 50.7% 0.076600 0.082569 47.3% 0.189509 0.195326 51.5% 0.077607 0.083577 47.9% 0.192004 0.197829 52.2% 0.078586 0.084559 48.6% 0.194440 0.200273 52.9% 0.079540 0.085514 49.3% 0.196815 0.202656 53.7% 0.080468 0.086443 50.0% 0.199128 0.204977 54.4% 0.081371 0.087348 50.7% 0.201378 0.207235 55.1% 0.082251 0.088228 51.4% 0.203564 0.209429 55.9% 0.083108 0.089087 52.1% 0.205684 0.211557 56.6% 0.083943 0.089923 52.7% 0.207737 0.213618 57.4% 0.084759 0.090739 53.4% 0.209723 0.215611 58.1% 0.085556 0.091537 54.1% 0.211639 0.217536 58.8% 0.086335 0.092318 54.8% 0.213486 0.219389 59.6% 0.087100 0.093083 55.5% 0.215261 0.221172 60.3% 0.087850 0.093834 56.2% 0.216963 0.222881 61.0% 0.088589 0.094573 56.8% 0.218592 0.224517 61.8% 0.089319 0.095303 57.5% 0.220147 0.226079 62.5% 0.090041 0.096025 58.2% 0.221625 0.227564 63.2% 0.090757 0.096742 58.9% 0.223027 0.228972 64.0% 0.091471 0.097455 59.6% 0.224351 0.230302 64.7% 0.092183 0.098168 60.3% 0.225596 0.231553 65.4% 0.092898 0.098882 61.0% 0.226761 0.232724 66.2% 0.093616 0.099601 61.6% 0.227845 0.233813 66.9% 0.094342 0.100326 62.3% 0.228848 0.234820 67.6% 0.095077 0.101060 63.0% 0.229767 0.235744 68.4% 0.095824 0.101807 63.7% 0.230603 0.236584 69.1% 0.096586 0.102568 64.4% 0.231353 0.237338 69.9% 0.097366 0.103347 65.1% 0.232019 0.238007 70.6% 0.098166 0.104146 65.8% 0.232597 0.238589 71.3% 0.098989 0.104968 66.4% 0.233089 0.239083 72.1% 0.099838 0.105816 67.1% 0.233493 0.239489 72.8% 0.100716 0.106692 67.8% 0.233808 0.239806 73.5% 0.101625 0.107599 68.5% 0.234034 0.240033 74.3% 0.102568 0.108540 69.2% 0.234170 0.240169 75.0% 0.103547 0.109518 69.9% 0.234215 0.240215 75.7% 0.104566 0.110534 70.5% 0.234170 0.240170 76.5% 0.105627 0.111592 71.2% 0.234034 0.240033 77.2% 0.106731 0.112694 71.9% 0.233807 0.239804 77.9% 0.107882 0.113841 72.6% 0.233487 0.239483 78.7% 0.109082 0.115037 73.3% 0.233076 0.239070 79.4% 0.110332 0.116283 74.0% 0.232574 0.238565 80.1% 0.111634 0.117582 74.7% 0.231979 0.237967 80.9% 0.112990 0.118934 75.3% 0.231293 0.237277 81.6% 0.114402 0.120341 76.0% 0.230516 0.236495 82.4% 0.115872 0.121806 76.7% 0.229647 0.235622 83.1% 0.117399 0.123328 77.4% 0.228688 0.234658 83.8% 0.118986 0.124909 78.1% 0.227639 0.233604 84.6% 0.120633 0.126551 78.8% 0.226501 0.232459 85.3% 0.122341 0.128252 79.5% 0.225274 0.231226 86.0% 0.124110 0.130015 80.1% 0.223960 0.229905 86.8% 0.125940 0.131839 80.8% 0.222559 0.228497 87.5% 0.127831 0.133723 81.5% 0.221072 0.227002 88.2% 0.129783 0.135669 82.2% 0.219500 0.225423 89.0% 0.131795 0.137674 82.9% 0.217845 0.223760 89.7% 0.133867 0.139739 83.6% 0.216108 0.222015 90.4% 0.135998 0.141863 84.2% 0.214290 0.220188 91.2% 0.138186 0.144044 84.9% 0.212392 0.218282 91.9% 0.140430 0.146281 85.6% 0.210416 0.216297 92.6% 0.142729 0.148574 86.3% 0.208362 0.214235 93.4% 0.145081 0.150919 87.0% 0.206233 0.212097 94.1% 0.147485 0.153316 87.7% 0.204029 0.209884 94.9% 0.149938 0.155762 88.4% 0.201752 0.207597 95.6% 0.152439 0.158257 89.0% 0.199401 0.205237 96.3% 0.154985 0.160797 89.7% 0.196979 0.202804 97.1% 0.157576 0.163382 90.4% 0.194484 0.200300 97.8% 0.160209 0.166008 91.1% 0.191918 0.197724 98.5% 0.162882 0.168676 91.8% 0.189280 0.195075 99.3% 0.165595 0.171383 92.5% 0.186569 0.192354 100.0% 0.167181 0.172966 93.2% 0.183784 0.189557 93.8% 0.180923 0.186685 94.5% 0.177984 0.183733 95.2% 0.174963 0.180698 95.9% 0.171855 0.177577 96.6% 0.168656 0.174362 97.3% 0.165360 0.171047 97.9% 0.161957 0.167625 98.6% 0.158439 0.164086 99.3% 0.154795 0.160417 100.0% 0.154190 0.159809

In an embodiment, the ratio between the sag values at 75 percent point and at 25 percent point of the imaging-side surface of third lens element 5 satisfies the following condition:

5.0<sag8(75)/sag8(25)<7.0   (1)

where sag8(75) is the sag value at 75 percent point of the clear aperture of the imaging-side of the third lens element measured from the optical axis, and sag8(25) is the sag value at 25 percent point of the clear aperture of the imaging-side of the third lens element. In some embodiments, the ratio between the sag values at 75 percent point and at 25 percent point of the imaging-side surface of third lens element 5 in Equation (1) is preferably in a range from 5.5 to 6.5.

In an exemplary embodiment, the imaging-side surface of third lens element 5 has a sag at the 25 percent point from the optical axis of about 38 microns and a sag at the 75 percent point from the optical axis of about 245 microns. If the ratio in condition (1) exceeds the upper limit, the optical power of the third lens element and the lens system 300 may be reduced. If the ratio in condition (1) is smaller than the lower limit, the compactness of the lens system 200 (FIG. 2) may be affected.

Additionally, the object-side surface of fourth lens element 6 has a sag value at 100 percent point satisfying the following condition:

sag9(100)>167 microns   (2)

where sag9(100) is the sag value at 100 percent point of the clear aperture measured from the optical axis of the object-side surface of the fourth lens element (see Table 5 and FIG. 4).

Furthermore, the imaging-side surface of fourth lens element 6 provides the largest sag value at a certain percentage point of the effective radius. In an embodiment, the largest sag value is 235 microns at 75 percentage point of the efficient radius of the fourth lens element. That is, the imaging-side surface of the fourth lens element satisfies the following condition:

sag10(max)>235 microns   (3)

where sag10(max) denotes the highest sag value of the imaging-side surface of the fourth lens element.

If the imaging-side surface of the fourth lens element does not meet the condition (3), the lens system 200 of FIG. 2 may have astigmatism and aberration that exceeds the target design specifications. In some embodiments, the conditions (1), (2) and (3) allow the system to be constructed with a target total track length.

In an embodiment, first, second, third and fourth lens elements can be made of plastic or glass and have an Abbe number of about 56, 23, 56, and 56, respectively. In an embodiment, the lens system 200 satisfies the following design characteristics and conditions:

vd1−vd2>30;   (4)

0.5<d1avg/d2avg<0.9;   (5)

0.4<d3avg/d4avg<0.7   (6)

wherein vd1, vd2 are the respective Abbe number of the first and second lens elements, and d1avg, d2avg, d3avg, and d4avg are the respective average diameters of the first, second, third, and fourth lens elements. The average diameter is the sum of the object-side and imaging-side diameters of a lens element, divided by two.

In order to obtain a high-performance lens system which is suitable ofr mega-pixels imaging sensors, the range in Equation (6) may be narrower such as 0.45<d3avg/d4avg<0.65, or preferably 0.50<d3avg /d4avg<0.60.

Air gaps between the lens elements and optical filter may minimize aberrations. In a preferred embodiment, the ratio between the sum of all air gaps from the imaging-side surface of the first lens element to the object-side surface of the optical filter and the total track length (TTL) is less than 0.4 in order for the lens system to be able to focus from infinity to portrait distances. In order words, the lens system 200 satisfies the following condition:

(Σ(air gaps))/TTL<0.4   (7)

where Σ(air gaps) is the sum of all air gaps from the imaging-side surface of the first lens element to the object-side surface of the optical filter and TTL is the total track length of the lens system. In some embodiments, the upper limit in Equation (7) may be smaller such as less than 0.35 or preferably than 0.3 to obtain a compacter design of the lens system.

Similarly, air gaps between the lens elements may minimize aberrations. In some embodiments, the ratio between the sum of all air gaps between lens elements and the total track length (TTL) is less than 0.25 in order for the lens system to be able to focus from infinity to portrait distances. In a preferred embodiment, the sum of the air gaps from the imaging-side surface of the first lens element to the object-side surface of the fourth lens element is about 0.5 mm. The ratio of the sum of the air gaps between the lens elements to the total track length is about 0.25 or less, or preferably about 0.2 or less.

The relative positions of the lens elements to each other contribute to good optical performance. In some embodiments, the air gaps satisfy the following inequities:

0<s1/s2<0.4   (8)

0<s3/s4<0.2   (9)

wherein s1 is the air gap between the imaging-side surface of first lens element 3 and the object-side surface of second lens element 4, s2 is the air gap between the imaging-side surface of second lens element 4 and the object-side surface of third lens element 5, s3 is the air gap between the imaging-side surface of third lens element 5 and the object-side surface of fourth lens element 6, and s4 is the air gap between the imaging-side surface of fourth lens element 6 and the object-side surface of optical filter 7, as shown in FIG. 3.

Further, the average diameter of each of the lens elements is related to its thickness as follows:

2<d1avg/t1<3;   (10)

4<d2avg/t2<6   (11)

3<d3avg/t3<4   (12)

8<d4avg/t4<10   (13)

wherein t1, t2, t3, and t4 are the respective thickness of the first, second, third, and fourth lens elements, and d1avg, d2avg, d3avg, and d4avg are the respective average diameters of the first, second, third, and fourth lens elements. (As noted above, the average diameter is the sum of the object-side diameter and the imaging-side diameter of a lens element, divided by two.)

FIG. 5 is a schematic diagram illustrating TV distortion of an imaging lens system. TV distortion causes deviation from an ideal rectangular image field 500, which can occur as an inward distortion 502 or outward distortion 504. A TV distortion can be expressed with the following equation:

TV distortion=Δh/h   (16)

In some embodiments, an imaging lens system as described herein may have performance of astigmatism and distortion aberrations that meet certain target characteristics. Images taken with an imaging lens system disclosed above can be viewed on a TV screen with a TV distortion of less than 1 percent.

FIG. 6 shows a relation between a semiconductor imaging sensor (e.g., a CMOS imaging sensor), the associated sensor image circle and the maximum image circle according to an embodiment of the present invention. The sensor image circle (SIC) can be defined as a circle 600 that circumscribes a rectangular imaging sensor 602. In other words, the diameter of sensor image circle is equal to a diagonal size 603 of the rectangular imaging sensor. The maximum image circle for a lens system can be defined as a circle 604 that corresponds to a circular area in the imaging plane over which the lens produces acceptable image quality. In some embodiments, the ratio between the sensor image circle and the maximum image circle is greater than 0.9. For example, the imaging sensor may have a diagonal of about 3.22 mm, so that the sensor image circle also has a diameter of 3.22 mm, and the maximum image circle has a diameter of 3.44 mm. In an embodiment, the lens system has a chief ray angle of less than 28° and a relative illumination at full field diagonal image height greater than 40 percent. Embodiments of the present invention provide a compact lens system according to the following inequity:

DM/TTL≧1.0   (17)

where DM is the diameter of the sensor image circle and TTL is the total track length. For example, the sensor image circle can have a diameter of 3.22 mm and the total track length can be 3.10 mm in one embodiment.

In some embodiments, illumination of the surface area of the imaging sensor may depend on performance characteristics of an associated lens system. In general, an optical lens system may not illuminate the imaging sensor uniformly even when a uniform illuminating light is applied to it. A lens system may only partially pass through light that irradiates the lens system at a certain angle of incidence. The lens system may completely pass light that is substantially normal to the optical axis. As a result, the imaging sensor may receive more light in the center than around the edges. Therefore, a relative illumination may be used to characterize the optical performance of a lens system. The relative illumination can be defined as a percentage of a maximum illumination value. If the maximum illumination value of a surface region (e.g., the center) of the imaging sensor is 1.0 or 100%, the relative illumination values may decrease when moving away from the center of the imaging sensor. In an embodiment, the lens system 200 or 300 as shown in FIG. 2 or 3 may provide a relative illumination value greater than 40.0 percent across the diagonal of the imaging sensor.

While the invention has been described with respect to specific embodiments, one skilled in the art will recognize that variations and modifications are possible and that the invention is intended to cover all modifications and equivalents within the scope of the following claims. 

What is claimed is:
 1. An imaging lens comprising first, second, third, and fourth lens elements arranged in order from an object side to an imaging side, each of the first, second, third, and fourth lens elements having an object side surface facing toward the object side, and an imaging side surface facing toward the imaging side, wherein, 30<vd1−vd2; 0.4<d3avg/d4avg<0.7; and a ratio of a ratio between a sag at 5 percent point and a sag at 100 percent point of the imaging-side surface of the first lens element is in a range from −0.0082 to 0.0114.
 2. The lens system of claim 1 where in a ratio of a ratio between a sag at 6 percent point and a sag at 100 percent point of the imaging-side surface of the second lens element is in a range from −0.0025 to 0.01.
 3. The lens system of claim 1 wherein the first, second, third, and fourth lens elements have air gaps therebetween and a ratio of a total air gap to a total track length is about 0.25 or less.
 4. The lens system of claim 1 further satisfying the following equations: 0<s1/s2<0.4; and 0<s3/s4<0.2; wherein s1 is an air gap between the imaging side surface of the first lens element and the object side surface of the second lens element, s2 is an air gap between the imaging side surface of the second lens element and the object side surface of the third lens element, s3 is an air gap between the imaging side surface of the third lens element and the object side surface of the fourth lens element, s4 is an air gap between the imaging side surface of the fourth lens element and the object side surface of the optical filter.
 5. The lens system of claim 4 wherein the imaging-side surface of the fourth lens element has a maximum sag in a range of 235 microns to 240 microns at the proximity of a 75 percent point in relation to the optical axis.
 6. The lens system of claim 1 wherein the imaging-side surface of the fourth lens element has a maximum sag greater than 235 microns.
 7. The lens system of claim 1 wherein the lens system has a maximum chief ray angle (CRA) smaller than 28°.
 8. The lens system of claim 1 wherein the lens system has a TV distortion smaller than 1.0 percent.
 9. An imaging lens comprising first, second, third, and fourth lens elements arranged in order from an object side to an imaging side, each of the first, second, third, and fourth lens elements having an object side surface facing toward the object side, and an imaging side surface facing toward the imaging side, the imaging lens satisfies the conditions of: 30<vd1−vd2; 0.5<d1avg/d2avg <0.9; and 0.4<d3avg/d4avg<0.7.
 10. The lens system of claim 9 wherein a sag at 100 percent point of the maximum clear aperture of the imaging-side surface of the third lens element is equal to or greater than 300 microns.
 11. The lens system of claim 9 wherein the first lens element has a ratio of average diameter to thickness in a range from 2 to
 3. 12. The lens system of claim 9 further satisfying the following condition: DM/TTL≧1.0, wherein DM is a diameter of a sensor image circle and TTL is a total track length.
 13. The lens system of claim 9 further comprising a relative illumination greater than 40.0 percent across a full diagonal size of an imaging sensor.
 14. The lens system of claim 9 wherein a ratio of a ratio between a sag at 5 percent point and a sag at 100 percent point of the imaging-side surface of the first lens element is in a range from −0.0082 to 0.0114.
 15. The lens system of claim 14 wherein a sag at 100 percent point of the maximum clear aperture of the object-side surface of the fourth lens element is equal to or greater than 167 microns. 